Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 860747, 7 pages.

Price of Fairness on Networked Auctions

Mariusz Kaleta

Full-text: Open access

Abstract

We consider an auction design problem under network flow constraints. We focus on pricing mechanisms that provide fair solutions, where fairness is defined in absolute and relative terms. The absolute fairness is equivalent to “no individual losses” assumption. The relative fairness can be verbalized as follows: no agent can be treated worse than any other in similar circumstances. Ensuring the fairness conditions makes only part of the social welfare available in the auction to be distributed on pure market rules. The rest of welfare must be distributed without market rules and constitutes the so-called price of fairness. We prove that there exists the minimum of price of fairness and that it is achieved when uniform unconstrained market price is used as the base price. The price of fairness takes into account costs of forced offers and compensations for lost profits. The final payments can be different than locational marginal pricing. That means that the widely applied locational marginal pricing mechanism does not in general minimize the price of fairness.

Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 860747, 7 pages.

Dates
First available in Project Euclid: 1 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1412178170

Digital Object Identifier
doi:10.1155/2014/860747

Mathematical Reviews number (MathSciNet)
MR3240639

Citation

Kaleta, Mariusz. Price of Fairness on Networked Auctions. J. Appl. Math. 2014, Special Issue (2014), Article ID 860747, 7 pages. doi:10.1155/2014/860747. https://projecteuclid.org/euclid.jam/1412178170


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References

  • M. Kaleta, “Security constrained network winner determination problem,” in Automatyzacja Procesów Dyskretnych, Teoria i Zastosowania, A. Świerniak and J. Krystek, Eds., pp. 111–118, Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego, 2012.
  • M. Kaleta and T. Traczyk, Modeling Multi-Commodity Trade: Information Exchange Methods, Advances in Intelligent and Soft Computing, Springer, 2012.
  • H. Cremer and J. Laffont, “Competition in gas markets,” European Economic Review, vol. 46, no. 4-5, pp. 928–935, 2002.
  • H. Cremer, F. Gasmi, and J. Laffont, “Access to pipelines in competitive gas markets,” Journal of Regulatory Economics, vol. 24,no. 1, pp. 5–33, 2003.
  • A. Dinar, R. Howitt, S. Rassenti, and V. L. Smith, “Development of water markets using experimental economics,” in Markets for Water, K. Easter, M. Rosegrant, and A. Dinar, Eds., vol. 15of Natural Resource Management and Policy, pp. 259–275, Springer, New York, NY, USA, 1998.
  • P. Kacprzak, M. Kaleta, P. Pałka, K. Smolira, E. Toczyłowski, and T. Traczyk, “Application of open multi-commodity market data model on the communication bandwidth market,” Journal ofTelecommunications and Information Technology, vol. 4, pp. 45–50, 2007.
  • F. C. Schweppe, M. C. Caramanis, R. D. Tabors, and R. E. Bohn, Spot Pricing of Electricity, Kluwer Academic Publishers, New York, NY, USA, 1988.
  • W. W. Hogan, “Contract networks for electric power transmission,” Journal of Regulatory Economics, vol. 4, no. 3, pp. 211–242, 1992.
  • S. Lochner, “Identification of congestion and valuation of transport infrastructures in the European natural gas market,” Energy, vol. 36, no. 5, pp. 2483–2492, 2011.
  • A. Rosenberg, “A proposed alternative to locational marginal pricing and its impact on new generation,” The Electricity Jour-nal, vol. 17, no. 3, pp. 11–25, 2004.
  • H. Luss, “On equitable resource allocation problems: a lexicographic minimax approach,” Operations Research, vol. 47, no. 3, pp. 361–378, 1999.
  • W. Ogryczak, M. Pioro, and A. Tomaszewski, “Telecommunications network design and max-min optimization problems,” Journal of Telecommunications and Information Technology, vol. 4, pp. 43–53, 2005.
  • H. Luss, Equitable Resource Allocation: Models, Algorithms and Applications, Information and Communic ation Technology Series, Wiley, 2012.
  • H. P. Young, Equity: In Theory and Practice, Princeton University Press, 1995.
  • A. B. Atkinson, “On the measurement of inequality,” Journal of Economic Theory, vol. 2, pp. 244–263, 1970.
  • A. Sen, On Economic Inequality, Clarendon Paperbacks, Clarendon Press, 1973.
  • W. Ogryczak, “Inequality measures and equitable locations,” Annals of Operations Research, vol. 167, pp. 61–86, 2009.
  • O. Maimon, “The variance equity measure in locational decision theory,” Annals of Operations Research, vol. 6, no. 5, pp. 147–160, 1986.
  • E. Erkut, “Inequality measures for location problems,” Location Science, vol. 1, no. 3, pp. 199–217, 1993.
  • W. Ogryczak and T. Trzaskalik, “Equity, fairness and multicriteria optimization,” in Multiple Criteria Decision Making '05, pp. 185–199, Wydawnictwo Uczelniane AE Katowice, 2006.
  • M. M. Kostreva and W. Ogryczak, “Linear optimization with multiple equitable criteria,” RAIRO Operations Research, vol. 33, no. 3, pp. 275–297, 1999.
  • V. Krishna and V. Krishna, Auction Theory, Academic Press, 2002.
  • S. Sudeendra, M. Saini, and S. Rao, “Fairness in combinatorial auctions,” CoRR abs/1005.4774, 2010.
  • J. Murillo, B. López, V. Muñoz, and D. Busquets, “Fairness in recurrent auctions with competing markets and supply fluctuations,” Computational Intelligence, vol. 28, no. 1, pp. 24–50, 2012.
  • C.-C. Wu, C.-C. Chang, and I.-C. Lin, “New sealed-bid electronic auction with fairness, security and efficiency,” Journal of Computer Science and Technology, vol. 23, no. 2, pp. 253–264, 2008.
  • E. Toczyłowski, Optimization of Market Processes under Constraints, EXIT Academic Publishing, 2003, (Polish).
  • D. Bertsimas, V. F. Farias, and N. Trichakis, “The price of fairness,” Operations Research, vol. 59, no. 1, pp. 17–31, 2011.
  • T. Bonald and L. Massouli, “Impact of fairness on internet performance,” in Proceedings of the ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS '01), pp. 82–91, ACM, New York, NY, USA, 2001.
  • M. Butler and H. P. Williams, “Fairness versus efficiency in charging for the use of common facilities,” Journal of the Operational Research Society, vol. 53, no. 12, pp. 1324–1329, 2002.
  • J. Mo and J. Walrand, “Fair end-to-end window-based congestion control,” IEEE/ACM Transactions on Networking, vol. 8, no. 5, pp. 556–567, 2000.
  • E. Toczyłowski and I. Zoltowska, “A new pricing scheme for a multi-period pool-based electricity auction,” European Journal of Operational Research, vol. 197, no. 3, pp. 1051–1062, 2009.
  • E. Koutsoupias and C. Papadimitriou, “Worst-case equilibria,” in Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, pp. 404–413, Trier, Germany, March 1999.
  • C. Papadimitriou, “Algorithms, games, and the internet,” in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC '01), pp. 749–753, ACM Press, New York, NY, USA, 2001.
  • M. Kaleta, “Computing alpha-efficient cost allocations for unbalanced games,” in Social Informatics, vol. 6430 of Lecture Notes in Computer Science, pp. 103–112, 2010. \endinput